LINEAR FUNCTIONS
TYPES OF LINES
1. INCREASING
2. DECREASING
3. SPECIAL
• HORIZONTAL
• VERTICAL
WHAT IS GRADIENT?
IT IS THE SLOPE OF THE LINE
It is always a number.
WHAT IS THE GRADIENT OF AN
INCREASING LINE?
THE GRADIENT IS ALWAYS
POSITIVE
WHAT IS THE GRADIENT OF
A DECREASING LINE?
THE GRADIENT IS ALWAYS
NEGATIVE
WHAT IS THE GRADIENT OF
A HORIZONTAL LINE?
THE GRADIENT IS ZERO
WHAT IS THE GRADIENT OF
A VERTICAL LINE?
THE GRADIENT IS
UNDEFINED
HOW TO FIND THE
GRADIENT?
USE TWO OBVIOUS POINTS (CAN BE GIVEN,
FROM A TABLE, FROM THE GRAPH)
𝑷𝟏 𝒙𝟏 , 𝒚𝟏
AND 𝑷𝟐 𝒙𝟐 , 𝒚𝟐
THEN USE THE RULE TO FIND THE GRADIENT
𝒚𝟐 − 𝒚𝟏
𝒎=
𝒙𝟐 − 𝒙𝟏
WHAT IS THE GRADIENT
FORM OF A LINEAR
FUNCTION?
𝑦 = 𝒎𝑥 + 𝒄
Where m is the gradient and c is the y-intercept.
WHAT IS THE STANDARD FORM
OF A LINEAR FUNCTION?
𝒂𝒙 + 𝒃𝒚 = 𝒄
HOW CAN WE TELL IF A POINT IS
ON THE LINE, WITHOUT GRAPHING
THE LINE?
SUBSTITUTE THE COORDINATES
OF THE POINT INTO THE RULE.
WHAT IS THE Y-INTERCEPT?
IT IS A POINT WHERE THE LINE CUTS THE
Y-AXIS.
THE X-COORDINATE OF THE Y-INTERCEPT
IS ALWAYS ZERO.
WHAT IS THE X-INTERCEPT?
IT IS A POINT WHERE THE LINE CUTS THE
X-AXIS.
THE Y-COORDINATE OF THE X-INTERCEPT
IS ALWAYS ZERO.
WHAT IS THE EQUATION OF
A HORIZONTAL LINE?
y = number
WHAT IS THE EQUATION OF
A VERTICAL LINE?
x = number
WHAT IS THE EQUATION OF
THE X-AXIS?
y=0
WHAT IS THE EQUATION OF
THE Y-AXIS?
x=0
HOW TO GRAPH A LINE IN GRADIENT
FORM?
THE EASIEST METHOD IS TO
USE TABLE OF VALUES.
HOW TO GRAPH A LINE IN
STANDARD FORM?
USE THE x and y INTERCEPT METHOD
• TO FIND THE X-INTERCEPT MAKE Y = 0
• TO FIND THE Y-INTERCEPT MAKE X = 0
HOW TO GRAPH SPECIAL LINES?
NO WORK IS NEEDED.
JUST SKETCH THEM.
WHAT IS SPECIAL ABOUT THE
GRADIENTS OF PARALLEL LINES?
THE GRADIENTS ARE THE SAME.
𝒎 𝟏 = 𝒎𝟐
WHAT IS SPECIAL ABOUT THE
GRADIENTS OF PERPENDICULAR
LINES?
THE PRODUCT OF THEIR
GRADIENTS IS THE SAME.
𝒎𝟏 × 𝒎𝟐 = −𝟏